Use a calculator to find the approximate value of the following expression if possible. Express your answers in radians and round to the hundredths. sin ¹ (2.12) 7.01 radians 5.01 radians Impossible since the value is not in the domain of sin¹ (x). 0.12 radians
Use a calculator to find the approximate value of the following expression if possible. Express your answers in radians and round to the hundredths. sin ¹ (2.12) 7.01 radians 5.01 radians Impossible since the value is not in the domain of sin¹ (x). 0.12 radians
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Finding the Approximate Value of the Inverse Sine Function**
**Problem Statement:**
Use a calculator to find the approximate value of the following expression if possible. Express your answers in radians and round to the hundredths.
\[ \sin^{-1}(2.12) \]
**Options:**
- A) 7.01 radians
- B) 5.01 radians
- C) Impossible since the value is not in the domain of \( \sin^{-1}(x) \)
- D) 0.12 radians
---
**Explanation:**
To solve this problem, it is important to recognize the domain of the inverse sine function, \( \sin^{-1}(x) \). The domain of \( \sin^{-1}(x) \) is \([-1, 1]\). This means that \( \sin^{-1}(x) \) is only defined for values of \( x \) within this interval.
Given the value 2.12, we note that this value is outside the domain of \( \sin^{-1}(x) \).
Therefore, the correct answer is:
- C) Impossible since the value is not in the domain of \( \sin^{-1}(x) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f130582-8262-45ba-b1cd-6680cc0034f3%2Fb83632bb-4ee8-4e41-8cae-ead5d31d564c%2Fdwbin2r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Approximate Value of the Inverse Sine Function**
**Problem Statement:**
Use a calculator to find the approximate value of the following expression if possible. Express your answers in radians and round to the hundredths.
\[ \sin^{-1}(2.12) \]
**Options:**
- A) 7.01 radians
- B) 5.01 radians
- C) Impossible since the value is not in the domain of \( \sin^{-1}(x) \)
- D) 0.12 radians
---
**Explanation:**
To solve this problem, it is important to recognize the domain of the inverse sine function, \( \sin^{-1}(x) \). The domain of \( \sin^{-1}(x) \) is \([-1, 1]\). This means that \( \sin^{-1}(x) \) is only defined for values of \( x \) within this interval.
Given the value 2.12, we note that this value is outside the domain of \( \sin^{-1}(x) \).
Therefore, the correct answer is:
- C) Impossible since the value is not in the domain of \( \sin^{-1}(x) \)
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